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1 T IME The notation of time External synchronization Internal synchronization Physical clocks and their synchronization Logical time and logical clocks 3

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1.1 S YNCHRONIZING P HYSICAL C LOCKS Computer each contains its physical clock. Physical clock is limited by its resolution - the period between updates of the clock register. Clock drift often happens to physical clocks. To compensate for clock drifts, computers are synchronized to a time service, e.g., UTC - Coordinated universal time. Several other algorithms for synchronization. 4

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1.1 C RISTIAN S C LOCK S YNCHRONIZATION A process P can record the total round-trip time T round taken to send the request m r and receive the reply m t. A simple estimate of the time to which P should set its clock is t + T round / 2. 5

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1.1 T HE B ERKELEY A LGORITHM A coordinator computer is chosen to act as the master. Master periodically polls to slaves whose clocks are to be synchronized. The master estimates their local clock times by observing the round-trip times, and it averages the values obtained. The master takes a fault-tolerant average. Should the master fail, then another can be elected to take over. 6

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1.1 T HE N ETWORK T IME P ROTOCOL NTP distributes time information to provide: a service to synchronize clients in Internet a reliable service that survives loss of connection a frequent resynchronization for clients clock drift protection against interference with time server NTP service is provided by various servers: Primary servers, secondary servers, and servers of other levels (called strata ). Synchronization subnet: the servers which are connected in a logical hierarchy. 7

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1.2 L OGICAL T IME AND L OGICAL C LOCKS The order of the events two events occurred in the order they appear in a process. event of sending occurred before event of receiving. happened-before relation, denoted by HB1 : If process p: x p y, then x y. HB2 : For any message m, send ( m ) rcv ( m ), HB3 : If x, y and z are events such that x y and y z, then x z. 8

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1.3 V ECTOR C LOCKS Vector clock A vector clock of N processes is an array of N integers Each process keeps its own vector clock V i, which it uses to timestamp a local event VC1: Initially, V i [ j ] = 0, for i, j = 1, 2…, N. VC2: Just before p i timestamps an event, it sets V i [ i ] := V i [ i ] + 1. VC3: p i includes the value t = V i in every message it sends. VC4: When p i receives a timestamp t in a message, it sets V i [ j ] := max ( V i [ j ], t [ j ]), for j = 1, 2…, N. Taking the component-wise maximum of two vector timestamps in this way is known as a merge operation. 12

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2.1 D ISTRIBUTED M UTUAL E XCLUSION The basic requirements for mutual exclusion: ME1 (safety): At most one process may execute in the critical section (CS) at a time. ME2 (liveness): A process requesting entry to the CS is eventually granted. ME3 (ordering): Entry to the CS should be granted in happened-before order. The central server algorithm. A ring-based algorithm. A distributed algorithm using logical clocks. 20

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2.2 E LECTIONS An election is a procedure carried out to choose a process from a group. A ring-based election algorithm. The bully algorithm. 21

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2.2.1 R ING -B ASED E LECTION A LGORITHM Each process P(i) has a communication channel to the next process P(i+1) mod N. Messages are sent clockwise. The goal is to elect a single process called the coordinator, which is the process with the largest identifier. 22

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2.2.2 B ULLY A LGORITHM The processes themselves are synchronous. I.e. they use timeouts to detect a process failure. Unlike the ring-based algorithm in which processes only know their neighbors, bully algorithm allows processes to know those processes with a higher identifier. There are three types of message: Election Answer Coordinator 121135 Coordinator is now 13, because it has the highest identifier 25

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2.2.2 B ULLY A LGORITHM The election begins when a process notices that the coordinator is failed. Several processes may discover this concurrently A process which detects the failure will send an election message to those with a higher identifier When a process receives an election message, it sends back an answer message and begins another election 121135 Election message Answer Message Election message Coordinator Process 12 will know that it is the highest identifier now as all its higher identifier process (i.e. process 13) have failed, this process will then send back the coordinator message to all its lower identifier process. 26

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3 M ULTICAST C OMMUNICATION Group (multicast) communication requires coordination and agreement. One multicast operation is much better than multiple send operation in terms of efficiency and delivery guarantees. Basic multicast: guarantees a correct process will eventually deliver the message. Reliable multicast: requires that all correct processes in the group must receive a message if any of them does. 27

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3.2.1 T OTAL, FIFO, C AUSAL O RDERING Let m 1 and m 2 be messages delivered to the group. Total ordering: Either m 1 is delivered before m 2 or m 2 is delivered before m 1, at all processes. Causal ordering: If m 1 happened-before m 2 then m 1 is delivered before m 2 at all processes. FIFO ordering: If m 1 is issued before m 2 then m 1 is delivered before m 2 at all processes. 31

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3.2.2 I MPLEMENTING M ESSAGE O RDERING Hold-back: A received message is not delivered until ordering constraints can be met. Stable message: all prior messages processed. Hold-back queue vs. delivery queue. Safety property: no message will be delivered out of order by being prematurely transferred. Liveness property: no message should wait on the hold-back queue forever. 33